William is 2 times as old as Omar. 28 years ago, William was 6 times as old as Omar. How old is William now?
Answer: We can use the given information to write down two equations that describe the ages of William and Omar. Let William's current age be $w$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $w = 2o$ 28 years ago, William was $w - 28$ years old, and Omar was $o - 28$ years old. The information in the second sentence can be expressed in the following equation: $w - 28 = 6(o - 28)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = w / 2$ . Substituting this into our second equation, we get: $w - 28 = 6($ $(w / 2)$ $- 28)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 28 = 3 w - 168$ Solving for $w$ , we get: $2 w = 140$ $w = \dfrac{1}{2} \cdot 140 = 70$.